• International Journal of Aeronautical and Space Sciences
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• v.2 no.2
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• pp.28-38
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• 2001

A numerical method for the assessment and correction of tunnel wall interference effects on forced-oscillation testing is presented. The method is based on the wall pressure signature method using computed wall pressure distributions. The wall pressure field is computed using unsteady three-dimensional full Navier-Stokes solver for a 70-degree pitching delta wing in a wind tunnel. Approximately-factorized alternate direction implicit (AF-ADI) scheme is advanced in time by solving block tri-diagonal matrices. The algebraic Baldwin-Lomax turbulence, model is included to simulate the turbulent flow effect. Also, dual time sub-iteration with, local, time stepping is implemented to improve the convergence. The computed wall pressure field is then imposed as boundary conditions for Euler re-simulation to obtain the interference flow field. The static computation shows good agreement with experiments. The dynamic computation demonstrates reasonable physical phenomena with a good convergence history. The effects of the tunnel wall in upwash and blockage are analyzed using the computed interference flow field for several reduced frequencies and amplitudes. The corrected results by pressure signature method agree well with the results of free air conditions.

• 유체기계공업학회:학술대회논문집
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• 2000.12a
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• pp.169-175
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• 2000

A design method for transonic turbine blades is developed based on Navier-Stokes equations. The present computing process is done on the four separate steps, 1.e., determination of the blade profile, generation of the computational grids, cascade flow simulation and analysis of the computed results in the sense of the aerodynamic performance. The blade shapes are designed using the cubic polynomials under the control of the design parameters. Numerical methods for the flow equations are based on Van-Leer's FVS with an upwind TVD scheme on the finite volume. Applications are made to the VKI transonic rotor blades. Computed results are analyzed with respect to the aerodynamic performance and are compared with the experimental data.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.2
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• pp.313-324
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• 1992

Two-dimensional Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system, then mapped into a generalized body-fitted coordinate system. All direction of viscous terms are incorporated and turbulent effects are modeled using the Baldwin-Lomax algebraic model. Equation are discretized using finite difference method on the C-type grids and solved using implicit LU-ADI decomposition scheme. Calculations are made at a VKI turbine cascade flow in a transonic wind-tunnel and compared to experimental data. Present numerical scheme is shown to be in good agreement with the previous experimental results and simulates the two-dimensional viscous flow phenomena.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1129-1163
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• 2013

Based on finite element discretization, two linearization approaches to the defect-correction method for the steady incompressible Navier-Stokes equations are discussed and investigated. By applying $m$ times of Newton and Picard iterations to solve an artificial viscosity stabilized nonlinear Navier-Stokes problem, respectively, and then correcting the solution by solving a linear problem, two linearized defect-correction algorithms are proposed and analyzed. Error estimates with respect to the mesh size $h$, the kinematic viscosity ${\nu}$, the stability factor ${\alpha}$ and the number of nonlinear iterations $m$ for the discrete solution are derived for the linearized one-step defect-correction algorithms. Efficient stopping criteria for the nonlinear iterations are derived. The influence of the linearizations on the accuracy of the approximate solutions are also investigated. Finally, numerical experiments on a problem with known analytical solution, the lid-driven cavity flow, and the flow over a backward-facing step are performed to verify the theoretical results and demonstrate the effectiveness of the proposed defect-correction algorithms.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.1
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• pp.120-126
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• 1991

An expanded scheme of a direct numerical solution method for solving the Navier-Stokes equation considering the modified boundary conditions for gas lubrication with ultra low clearance at high .LAMBDA. region is presented. Many examples are calculated by this scheme and their results are compared to the previous solutions using P$^{2}$H$^{[-992]}$ . This scheme has the advantages of fast calculation time and stable convergence in high .LAMBDA. region, and gives very good results in the case of fluid film thickness discontinuity.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.1950-1963
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• 1995

A modification of the approximate-factorization method is made to accelerate the convergency rate and to take sufficiently large Courant number without loss of accuracy. And a stable implicit finite-difference scheme for solving the incompressible Navier-Stokes equations employed above modified method is developed. In the present implicit scheme, the volume fluxes with contravariant velocity components and the pressure formulation in curvilinear coordinates is adopted. In order to satisfy the continuity condition completely and to remove spurious errors for the pressure, the Navier-Stokes equations are solved by a modified SMAC scheme using a staggered gird. The upstream-difference scheme such as the QUICK scheme is also employed to the right hand side. The implicit scheme is unconditionally stable and satisfies a diagonally dominant condition for scalar diagonal linear systems of implicit operator on the left hand side. Numerical results for some test calculations of the two-dimensional flow in a square cavity and over a backward-facing step are obtained using both usual approximate-factorization method and the modified one, and compared with each other. It is shown that the present scheme allows a sufficiently large Courant number of O(10$^{2}$) and reduces the computing time.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.377-381
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• 2006

Recently, as economy grow and population increase we need to develop our coastal area and make good use of it for various purposes. That's why large structures are being installed on the sea. Some samples are petroleum storage tanks, pier of sea bridges. These are large structures which have been installed at coastal area. When we design such vertical cylinder, we should avoid too much construction expense caused by excessive designing or by lack of sufficient design. In order to prevent excessive expenditure, it is important to correctly calculate the force of waves acting on structures and predict the wave transformation. In this study, apply to VOF method based on Navier-Stokes equation and then discussed that nonlinear wave force and wave transformation. A comparison between the numerical model and existing experimental results showed nice agreement among them.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.93-114
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• 2019

In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first-order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.173-192
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• 1999

We study a boundary optimal control problem of the fluid flow governed by the Navier-Stokes equations. the control problem is formulated with the flow through a channel with steps. The first-order optimality condition of the optimal control is derived. Finite element approximations of the solutions of the optimality system are defined and optimal error estimates are derived. finally, we present some numerical results.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.141-146
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• 1998

An Euler/Navier Stokes solver has been developed for the analysis of steady and unsteady flows. The $q-{\omega}$ turbulent model has been incorporated into the solver in strongly coupled manner for stability and robustness. A new Chimera hole cutting algorithm, Cut-paste algorithm, has been devised for automatic Chimera hole cutting. Number of viscous/inviscid numerical computations demonstrate the accuracy and the versatility of the solver.